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2022 | OriginalPaper | Chapter

Critical Points Properties of Ordinary Differential Equations as a Projection of Implicit Functions Using Spatio-temporal Taylor Expansion

Author : Vaclav Skala

Published in: Computational Science and Its Applications – ICCSA 2022

Publisher: Springer International Publishing

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Abstract

This contribution describes a new approach to formulation of ODE and PDE critical points using implicit formulation as t-variant scalar function using the Taylor expansion. A general condition for the critical points is derived and specified for t invariant case. It is expected, that the given new formulae lead to more reliable detection of critical points especially for large 3D fluid flow data acquisition, which enable high 3D vector compression and their representation using radial basis functions (RBF).

In the case of vector field visualization, e.g. fluid flow, electromagnetic fields, etc., the critical points of ODE are critical for physical phenomena behavior.

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It should be noted that in the case of the PDE the coordinates\(\mathbf {x}\) are as sumed to be time independent.

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Title: Critical Points Properties of Ordinary Differential Equations as a Projection of Implicit Functions Using Spatio-temporal Taylor Expansion
Author: Vaclav Skala
Publisher: Springer International Publishing
Book: Computational Science and Its Applications – ICCSA 2022
Print ISBN: 978-3-031-10449-7

Electronic ISBN: 978-3-031-10450-3

Copyright Year: 2022
DOI: https://doi.org/10.1007/978-3-031-10450-3_15

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